"to glance, look from a state of concealment" (especially through or as through a small or narrow opening), mid-15c., pepen, perhaps an alteration of Middle English piken (see peek (v.)). Hence, "to come partially into view, begin to appear" (1530s). Peeping Tom "a curious prying fellow" [Grose] is from 1796 (see Godiva).
"make a short chirp, cheap," as a bird, c. 1400, probably altered from pipen (mid-13c.), ultimately imitative (compare Latin pipare, French pepier, German piepen, Lithuanian pypti, Czech pipati, Greek pipos).
"a furtive look, as if through a crevice, a glimpse," 1520s, originally and especially "the first looking out of light from the eastern horizon" (the sense in peep of day); from peep (v.1). General meaning "a furtive glance" is attested by 1730.
"a short chirp, the cry of a mouse or young chick or other small bird," mid-15c., from peep (v.2); meaning "slightest sound or utterance" (usually in a negative context) is attested by 1903. Meaning "young chicken" is from 1680s. The marshmallow peeps confection are said to date from the 1950s.
He peeped at the woman through the window
he peeped his head through the window
the new moon peeped through the tree tops